Open Access
2025 Convergence rate for order 1 Markov random walks
Peter Gaydarov
Author Affiliations +
Electron. Commun. Probab. 30: 1-12 (2025). DOI: 10.1214/24-ECP652

Abstract

We examine the limiting behaviour of an order 1 Markov random walk in R2, i.e. a walk that remembers its previous step. Provided a certain symmetry of the Markovian condition, under relatively mild conditions we prove convergence to a Brownian motion and bound the rate of convergence. Therefore, an order 1 Markov condition is insufficient to alter the limiting behaviour of a random walk.

Citation

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Peter Gaydarov. "Convergence rate for order 1 Markov random walks." Electron. Commun. Probab. 30 1 - 12, 2025. https://doi.org/10.1214/24-ECP652

Information

Received: 16 October 2023; Accepted: 30 December 2024; Published: 2025
First available in Project Euclid: 22 January 2025

Digital Object Identifier: 10.1214/24-ECP652

Subjects:
Primary: 60F05 , 60G50 , 60J05

Keywords: Brownian motion , convergence , convergence rate , Markov chain , Random walk

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